In search of those numbers
Let be distinct digits of a six digit number . When this number is multiplied by , the result is another six digit number . Find the sum of all possible values of .
The answer is 4.
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1 solution
Write n = A B C D E , so that ( 1 0 n + F ) F = 1 0 0 0 0 0 F + n .
Rearranging, this gives n = 1 0 F − 1 F ( 1 0 0 0 0 0 − F ) .
There are only 9 possible values of F . Checking these, we find only 1 and 4 give integer values for n ; and only F = 4 gives a value of n with distinct digits.